Multigrid Preconditioned Solver

The preconditioned solver example.

Kind: preconditioners
Builds on: preconditioned-solver
Upstream source: examples/multigrid-preconditioned-solver/multigrid-preconditioned-solver.cpp in the Ginkgo repository.

Introduction

In this example, we first read in a matrix from a file. The preconditioned CG solver is enhanced with a multigrid preconditioner. The example features the generating time and runtime of the CG solver.

The commented program

#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <string>

#include <ginkgo/ginkgo.hpp>


int main(int argc, char* argv[])
{

Some shortcuts

    using ValueType = double;
    using IndexType = int;
    using vec = gko::matrix::Dense<ValueType>;
    using mtx = gko::matrix::Csr<ValueType, IndexType>;
    using cg = gko::solver::Cg<ValueType>;
    using mg = gko::solver::Multigrid;
    using pgm = gko::multigrid::Pgm<ValueType, IndexType>;

Print version information

    std::cout << gko::version_info::get() << std::endl;

    const auto executor_string = argc >= 2 ? argv[1] : "reference";

Figure out where to run the code

    std::map<std::string, std::function<std::shared_ptr<gko::Executor>()>>
        exec_map{
            {"omp", [] { return gko::OmpExecutor::create(); }},
            {"cuda",
             [] {
                 return gko::CudaExecutor::create(0,
                                                  gko::OmpExecutor::create());
             }},
            {"hip",
             [] {
                 return gko::HipExecutor::create(0, gko::OmpExecutor::create());
             }},
            {"dpcpp",
             [] {
                 return gko::DpcppExecutor::create(
                     0, gko::ReferenceExecutor::create());
             }},
            {"reference", [] { return gko::ReferenceExecutor::create(); }}};

executor where Ginkgo will perform the computation

    const auto exec = exec_map.at(executor_string)();  // throws if not valid

Read data

    auto A = share(gko::read<mtx>(std::ifstream("data/A.mtx"), exec));

Create RHS as 1 and initial guess as 0

    gko::size_type size = A->get_size()[0];
    auto host_x = vec::create(exec->get_master(), gko::dim<2>(size, 1));
    auto host_b = vec::create(exec->get_master(), gko::dim<2>(size, 1));
    for (auto i = 0; i < size; i++) {
        host_x->at(i, 0) = 0.;
        host_b->at(i, 0) = 1.;
    }
    auto x = vec::create(exec);
    auto b = vec::create(exec);
    x->copy_from(host_x);
    b->copy_from(host_b);

Calculate initial residual by overwriting b

    auto one = gko::initialize<vec>({1.0}, exec);
    auto neg_one = gko::initialize<vec>({-1.0}, exec);
    auto initres = gko::initialize<vec>({0.0}, exec);
    A->apply(one, x, neg_one, b);
    b->compute_norm2(initres);

copy b again

    b->copy_from(host_b);

Create multigrid factory

    std::shared_ptr<gko::LinOpFactory> multigrid_gen;
    multigrid_gen =
        mg::build()
            .with_mg_level(pgm::build().with_deterministic(true))
            .with_criteria(gko::stop::Iteration::build().with_max_iters(1u))
            .on(exec);
    const gko::remove_complex<ValueType> tolerance = 1e-8;
    auto solver_gen =
        cg::build()
            .with_criteria(gko::stop::Iteration::build().with_max_iters(100u),
                           gko::stop::ResidualNorm<ValueType>::build()
                               .with_baseline(gko::stop::mode::absolute)
                               .with_reduction_factor(tolerance))
            .with_preconditioner(multigrid_gen)
            .on(exec);

Create solver

    std::chrono::nanoseconds gen_time(0);
    auto gen_tic = std::chrono::steady_clock::now();
    auto solver = solver_gen->generate(A);
    exec->synchronize();
    auto gen_toc = std::chrono::steady_clock::now();
    gen_time +=
        std::chrono::duration_cast<std::chrono::nanoseconds>(gen_toc - gen_tic);

Add logger

    std::shared_ptr<const gko::log::Convergence<ValueType>> logger =
        gko::log::Convergence<ValueType>::create();
    solver->add_logger(logger);

Solve system

    exec->synchronize();
    std::chrono::nanoseconds time(0);
    auto tic = std::chrono::steady_clock::now();
    solver->apply(b, x);
    exec->synchronize();
    auto toc = std::chrono::steady_clock::now();
    time += std::chrono::duration_cast<std::chrono::nanoseconds>(toc - tic);

Calculate residual

    auto res = gko::as<vec>(logger->get_residual_norm());

    std::cout << "Initial residual norm sqrt(r^T r): \n";
    write(std::cout, initres);
    std::cout << "Final residual norm sqrt(r^T r): \n";
    write(std::cout, res);

Print solver statistics

    std::cout << "CG iteration count:     " << logger->get_num_iterations()
              << std::endl;
    std::cout << "CG generation time [ms]: "
              << static_cast<double>(gen_time.count()) / 1000000.0 << std::endl;
    std::cout << "CG execution time [ms]: "
              << static_cast<double>(time.count()) / 1000000.0 << std::endl;
    std::cout << "CG execution time per iteration[ms]: "
              << static_cast<double>(time.count()) / 1000000.0 /
                     logger->get_num_iterations()
              << std::endl;
}

Results

This is the expected output:

Initial residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
4.3589
Final residual norm sqrt(r^T r):
%%MatrixMarket matrix array real general
1 1
1.69858e-09
CG iteration count:     39
CG generation time [ms]: 2.04293
CG execution time [ms]: 22.3874
CG execution time per iteration[ms]: 0.574036

The plain program